Arsenal strengthened their Premier League title push with victory, restoring a five-point cushion at the top, while Chelsea's hopes of finishing in the top four suffered another setback.
All three goals came from corners. William Saliba headed Arsenal in front early on before an own goal from Piero Hincapie brought Chelsea level. The decisive moment arrived in the second half when Jurrien Timber struck from another corner to seal the points.
The major talking point came in the first half when a corner from Reece James struck Declan Rice on the arm as he wrestled for position at the near post. Chelsea players appealed, but referee Darren England waved play on and VAR did not intervene. The PGMOL later confirmed the decision, stating it was not deemed a punishable handball offence.
Rosenior hinted at his dissatisfaction. "It's not the first time it's happened to us. It doesn't seem to happen to other teams," he said afterwards. "That's all I'll say on that."
However, the Chelsea boss was clear that his team's shortcomings were decisive. Speaking to BBC Radio 5 Live, he said: "I'm frustrated and disappointed. If we don't eradicate the set-play issues and our discipline issues, then for all of the good things we do, we are not going to get what we want."
Chelsea have now gone three league matches without a win and have had seven red cards in the Premier League this season, with Pedro Neto the latest to be dismissed.
"Two things - discipline and defending set-plays," Rosenior added. "If we can do that, we can still have a very, very good season."
The defeat leaves Chelsea sixth, six points adrift of the Champions League places ahead of a crucial clash with Aston Villa on Wednesday. Arsenal, meanwhile, continue their title chase with a trip to Brighton.